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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 92736br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.u3 | 92736br1 | \([0, 0, 0, -3351, 33644]\) | \(89194791232/41136627\) | \(1919270469312\) | \([2]\) | \(122880\) | \(1.0516\) | \(\Gamma_0(N)\)-optimal |
| 92736.u2 | 92736br2 | \([0, 0, 0, -27156, -1699360]\) | \(741709148608/11431161\) | \(34133263847424\) | \([2, 2]\) | \(245760\) | \(1.3982\) | |
| 92736.u4 | 92736br3 | \([0, 0, 0, -2316, -4690096]\) | \(-57512456/397771269\) | \(-9501909159149568\) | \([2]\) | \(491520\) | \(1.7448\) | |
| 92736.u1 | 92736br4 | \([0, 0, 0, -432876, -109620880]\) | \(375523199368136/91287\) | \(2180652171264\) | \([2]\) | \(491520\) | \(1.7448\) |
Rank
sage: E.rank()
The elliptic curves in class 92736br have rank \(1\).
Complex multiplication
The elliptic curves in class 92736br do not have complex multiplication.Modular form 92736.2.a.br
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
